Opuscula Mathematica
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ISSN 1232-9274
e-ISSN: 2300-6919
Issue Date
2016
Volume
Vol. 36
Number
No. 2
Description
Journal Volume
Opuscula Mathematica
Vol. 36 (2016)
Projects
Pages
Articles
Bounds on the inverse signed total domination numbers in graphs
(2016) Atapour, Maryam; Norouzian, Sepideh; Sheikholeslami, Seyed Mahmoud; Volkmann, Lutz
Let $G=(V,E)$ be a simple graph. A function $f:V\rightarrow \{-1,1\}$ is called an inverse signed total dominating function if the sum of its function values over any open neighborhood is at most zero. The inverse signed total domination number of $G$, denoted by $\gamma_{st}^0(G)$, equals to the maximum weight of an inverse signed total dominating function of $G$. In this paper, we establish upper bounds on the inverse signed total domination number of graphs in terms of their order, size and maximum and minimum degrees.
Free probability on Hecke algebras and certain group C*-algebras induced by Hecke algebras
(2016) Cho, Ilwoo
In this paper, by establishing free-probabilistic models on the Hecke algebras $\mathcal{H}\left(GL_{2}(\mathbb{Q}_{p})\right)$ induced by $p$-adic number fields $\mathbb{Q}_{p}$, we construct free probability spaces for all primes $p$. Hilbert-space representations are induced by such free-probabilistic structures. We study $C^{*}$-algebras induced by certain partial isometries realized under the representations.
Monotone method for Riemann-Liouville multi-order fractional differential systems
(2016) Denton, Zachary
In this paper we develop the monotone method for nonlinear multi-order $N$-systems of Riemann-Liouville fractional differential equations. That is, a hybrid system of nonlinear equations of orders $q_i$ where $0 \lt q_i \lt 1$. In the development of this method we recall any needed existence results along with any necessary changes. Through the method's development we construct a generalized multi-order Mittag-Leffler function that fulfills exponential-like properties for multi-order systems. Further we prove a comparison result paramount for the discussion of fractional multi-order inequalities that utilizes lower and upper solutions of the system. The monotone method is then developed via the construction of sequences of linear systems based on the upper and lower solutions, and are used to approximate the solution of the original nonlinear multi-order system.
A two cones support theorem
(2016) Estrada, Ricardo
We show that if the Radon transform of a distribution $f$ vanishes outside of an acute cone $C_{0}$, the support of the distribution is contained in the union of $C_{0}$ and another acute cone $C_{1}$, the cones are in a suitable position, and $f$ vanishes distributionally in the direction of the axis of $C_{1}$, then actually supp $\operatorname*{supp}f\subset C_{0}$. We show by examples that this result is sharp.
Solutions of fractional nabla difference equations - existence and uniqueness
(2016) Jonnalagadda, Jagan Mohan
In this article, we discuss existence, uniqueness and dependency of solutions of nonlinear fractional nabla difference equations in a Banach space equipped with a suitable norm, using the contractive mapping approach. As an application of the established results we present and analyse a few examples.